having a period of 16.17 years Convert this period Into seconds (1y-3.16x10 seco
ID: 304943 • Letter: H
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having a period of 16.17 years Convert this period Into seconds (1y-3.16x10 seconds) (seconds) b) Finding the semi-major axis, a. The angular size of the orbit of the star SO-2 is 0.165 Convert the angular size of the orbit in accsec into radians 206265 a The distance to the centre of the galaxy is given as 7 940 pc.Convert this distance into meters 7940 pcx (309x10?-- Find the major axis of the orblt using the formula: (1 mark) major-axis (m)-(angular size (rad))xdistance(m) Find the size of the semi-major axds by dividing major-axis+2 From Newton's Universal Gravitation Law, the mass of the supermassive black hole at the of our galaxy can be calculated with the formula Where G667x10-1 ags c) The mass of the Sun is approximately M, -1.99*10 kg Express the mass of the baick-hole in solar masses. (Hint calculate the ratio of the two manes) ? Compare the size of the semi-majoraxisa,ofthe solar to be sla, ofth, Solar System-ngth distance to the outer edge ofthe Kuiper Beltofabout SS All (1AU.LA%x10nm) e) Anumbezof recent publications give the mass of the central object of the Milky Way Galaxy as y 4 million times the mass of the Sun. How do your resultsExplanation / Answer
b) a = 9.813 x 1013 m
T = 16.17 x 3.16 x 107 = 510972000 s
G = 6.67 x 10-11 m3 kg-1 s-2
Putting the values of a and T in the Newton's equation, we get
M = ( 4 x (3.14)2 / (6.67 x 10-11) x (9.813 x 1013)3 ) / (510972000)2 = 2.14 x 1036
Thus, the mass of the black hole is 2.14 x 1036 kg.
c) M / Msun = (2.14 x 1036 ) / (1.99 x 1030) = 1.07 x 106
Thus, the mass of the black hole is 1.07 x 106 solar masses.
d) The semi-major axis of the SO-2 star's orbit, a = 9.813 x 1013 m
Size of the solar system, let's say b = 55 x 1.496 x 1011 = 8.22 x 1012 m
Thus, the size of the size of the semi-major axis is 11.92 times bigger than the size of the solar system, since
a / b = (9.813 x 1013 ) / (8.22 x 1012 ) = 11.92
e) The result obtained in part c) suggests that the mass of the central object in the Milky Way Galaxy is approximately 106, i.e. 1 million times the mass of the Sun.
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